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A081271
Vertical of triangular spiral in A051682.
6
1, 13, 34, 64, 103, 151, 208, 274, 349, 433, 526, 628, 739, 859, 988, 1126, 1273, 1429, 1594, 1768, 1951, 2143, 2344, 2554, 2773, 3001, 3238, 3484, 3739, 4003, 4276, 4558, 4849, 5149, 5458, 5776, 6103, 6439, 6784, 7138, 7501, 7873, 8254, 8644, 9043, 9451
OFFSET
0,2
COMMENTS
Lies to the right of the y-axis of the triangle.
Binomial transform of (1, 12, 9, 0, 0, 0, ...).
FORMULA
G.f.: (1 + 10*x - 2*x^2)/(1 - x)^3.
a(n) = binomial(n,0) + 12*binomial(n,1) + 9*binomial(n,2).
a(n) = (9*n^2 + 15*n + 2)/2.
a(0) = 1, a(n) = a(n-1) + 9*n + 3 for n > 0 - Gerald McGarvey, Aug 18 2004
From Elmo R. Oliveira, Oct 25 2024: (Start)
E.g.f.: exp(x)*(1 + 12*x + 9*x^2/2).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
PROG
(PARI) a(n)=(9*n^2+15*n+2)/2 \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
Cf. A062741, A283394 (see Crossrefs section).
Sequence in context: A134864 A093100 A292472 * A190458 A180673 A081752
KEYWORD
nonn,easy
AUTHOR
Paul Barry, Mar 15 2003
STATUS
approved