A160674 A bisection of A063522.

1, 63, 305, 847, 1809, 3311, 5473, 8415, 12257, 17119, 23121, 30383, 39025, 49167, 60929, 74431, 89793, 107135, 126577, 148239, 172241, 198703, 227745, 259487, 294049, 331551, 372113, 415855, 462897, 513359, 567361, 625023, 686465, 751807, 821169, 894671

Offset

0,2

Links

Table of n, a(n) for n=0..35.

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

From Elmo R. Oliveira, Apr 22 2026: (Start)

G.f.: (1 + x)*(1 + 58*x + x^2)/(1 - x)^4.

E.g.f.: (1 + 62*x + 90*x^2 + 20*x^3)*exp(x).

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).

a(n) = 20*n^3 + 30*n^2 + 12*n + 1 = A005408(n)*A069133(n+1). (End)

Mathematica

Table[LegendreP[3, 2n+1], {n, 0, 50}]

Prog

(PARI) a(n)=pollegendre(3, 2*n+1) \\ Charles R Greathouse IV, Mar 19 2017

Crossrefs

Cf. A005408, A063522, A069133, A160699.

Sequence in context: A359564 A138833 A204736 * A034817 A160895 A203556

Adjacent sequences: A160671 A160672 A160673 * A160675 A160676 A160677

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 17 2009

Status

approved