The On-Line Encyclopedia of Integer Sequences (OEIS)

Revisions by Chai Wah Wu (See also Chai Wah Wu's wiki page)

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A315681

Coordination sequence Gal.6.159.5 where Gal.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
(history; published version)

#5 by Chai Wah Wu at Fri Nov 15 11:15:41 EST 2024

STATUS

editing

proposed

#4 by Chai Wah Wu at Fri Nov 15 11:15:37 EST 2024

FORMULA

Conjectures from Chai Wah Wu, Nov 15 2024: (Start)

a(n) = a(n-1) + a(n-3) - a(n-4) - a(n-6) + a(n-7) + a(n-9) - a(n-10) for n > 10.

G.f.: (x^10 + 5*x^9 + 6*x^8 + 4*x^7 - x^5 + 4*x^3 + 6*x^2 + 5*x + 1)/(x^10 - x^9 - x^7 + x^6 + x^4 - x^3 - x + 1). (End)

STATUS

approved

editing

A375085

Triangle read by rows: T(n,k) is the number of ballotlike paths ending at (n, k), with 0 <= k <= n.
(history; published version)

#19 by Chai Wah Wu at Fri Nov 15 09:46:39 EST 2024

STATUS

editing

proposed

#18 by Chai Wah Wu at Fri Nov 15 09:46:34 EST 2024

PROG

def A375854A375085(n):

STATUS

approved

editing

A374441

Triangle read by rows: T(n, k) = binomial(n - floor(k/2), ceiling(k/2)) - binomial(n - ceiling(k/2), floor(k/2)).
(history; published version)

#22 by Chai Wah Wu at Thu Nov 14 16:14:28 EST 2024

STATUS

editing

proposed

#21 by Chai Wah Wu at Thu Nov 14 16:14:24 EST 2024

PROG

return comb(a-(b+1>>1), b+1>>1) if b&1 else 0 # Chai Wah Wu, Nov 14 2024

#20 by Chai Wah Wu at Thu Nov 14 16:14:12 EST 2024

PROG

(Python)

from math import isqrt, comb

def A374441(n):

a = (m:=isqrt(k:=n+1<<1))-(k<=m*(m+1))

b = n-comb(a+1, 2)

return comb(a-(b+1>>1), b+1>>1) if b&1 else 0 # Chai Wah Wu, Nov 14 2024

STATUS

approved

editing

A375085

Triangle read by rows: T(n,k) is the number of ballotlike paths ending at (n, k), with 0 <= k <= n.
(history; published version)

#11 by Chai Wah Wu at Thu Nov 14 16:08:51 EST 2024

STATUS

editing

proposed

#10 by Chai Wah Wu at Thu Nov 14 16:08:47 EST 2024

PROG

return int(binomial(c:=a-1<<1, d:=a-b-1)-binomial(c, d-1)+binomial(a-2, d+1)) if n else 0 # Chai Wah Wu, Nov 14 2024

#9 by Chai Wah Wu at Thu Nov 14 16:08:28 EST 2024

PROG

(Python)

from math import isqrt

from sympy import binomial

def A375854(n):

a = (m:=isqrt(k:=n+1<<1))-(k<=m*(m+1))

b = n-binomial(a+1, 2)

return int(binomial(c:=a-1<<1, d:=a-b-1)-binomial(c, d-1)+binomial(a-2, d+1)) if n else 0 # Chai Wah Wu, Nov 14 2024

STATUS

approved

editing