The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A063376 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A063376

a(-1) = 1; for n >= 0, a(n) = 2^n + 4^n = 2^n*(1 + 2^n).
(history; published version)

#79 by Charles R Greathouse IV at Thu Sep 08 08:45:03 EDT 2022

PROG

(MAGMAMagma) [1] cat [2^n + 4^n : n in [0..30]]; // Wesley Ivan Hurt, Jul 03 2020

Discussion

Thu Sep 08

08:45

OEIS Server: https://oeis.org/edit/global/2944

#78 by Alois P. Heinz at Fri Jul 03 23:34:26 EDT 2020

STATUS

reviewed

approved

#77 by Michel Marcus at Fri Jul 03 23:29:20 EDT 2020

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proposed

reviewed

#76 by Wesley Ivan Hurt at Fri Jul 03 18:48:34 EDT 2020

STATUS

editing

proposed

#75 by Wesley Ivan Hurt at Fri Jul 03 18:47:58 EDT 2020

FORMULA

a(n) = Sum_{k=0..n} if((n-k) mod 4 = 0, binomial(n, 2k2*k), 0)}. - Paul Barry, Sep 19 2005

a(n) = 4a4*a(n-1) - 2^n = 6a6*a(n-1) - 8a8*a(n-2) = A001576(n) - 1 = 2*A007582(n) = A005418(2n2*n+2) = A002378(A000079(n)).

PROG

(MAGMA) [1] cat [2^n + 4^n : n in [0..30]]; // Wesley Ivan Hurt, Jul 03 2020

STATUS

proposed

editing

#74 by Michael De Vlieger at Fri Jul 03 18:40:15 EDT 2020

STATUS

editing

proposed

#73 by Michael De Vlieger at Fri Jul 03 18:40:13 EDT 2020

LINKS

M. Archibald, A. Blecher, A. Knopfmacher, M. E. Mays, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL23/Archibald/arch3.html">Inversions and Parity in Compositions of Integers</a>, J. Int. Seq., Vol. 23 (2020), Article 20.4.1.

STATUS

approved

editing

#72 by Alois P. Heinz at Tue Jan 07 17:45:25 EST 2020

STATUS

editing

approved

#71 by Alois P. Heinz at Tue Jan 07 17:45:21 EST 2020

CROSSREFS

Cf. Essentially the same as A028402.

STATUS

approved

editing

#70 by Alois P. Heinz at Tue Jan 07 17:42:20 EST 2020

STATUS

editing

approved