A015225 Odd hexagonal pyramidal numbers.

1, 7, 95, 161, 525, 715, 1547, 1925, 3417, 4047, 6391, 7337, 10725, 12051, 16675, 18445, 24497, 26775, 34447, 37297, 46781, 50267, 61755, 65941, 79625, 84575, 100647, 106425, 125077, 131747, 153171, 160797, 185185, 193831, 221375, 231105

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,3,-3,-3,3,1,-1).

Formula

Odd numbers of the form n*(n+1)*(4n-1)/6.

From Ant King, Oct 25 2012: (Start)

a(n) = a(n-1) +3*a(n-2) -3*a(n-3) -3*a(n-4) +3*a(n-5) +a(n-6) -a(n-7).

a(n) = 3*a(n-2) -3*a(n-4) +a(n-6) +256.

a(n) = (8*n-2*(-1)^n-7)*(1+(-1)^n-4*n)*(3+(-1)^n-4*n)/24.

G.f.: x*(1+6*x+85*x^2+48*x^3+103*x^4+10*x^5+3*x^6) / ((1-x)^4*(1+x)^3). (End)

E.g.f.: (1/6)*(-9 - 6*x - 24*x^2 + 18*exp(x) + ( - 9 + 12*x + 36*x^2 + 32*x^3)*exp(2*x))*exp(-x). - G. C. Greubel, Jul 30 2016

Mathematica

LinearRecurrence[{1, 3, -3, -3, 3, 1, -1}, {1, 7, 95, 161, 525, 715, 1547}, 36] (* Ant King, Oct 25 2012 *)

Prog

(PARI) a(n)=(8*n-2*(-1)^n-7)*(1+(-1)^n-4*n)*(3+(-1)^n-4*n)/24 \\ Charles R Greathouse IV, Jul 30 2016

Crossrefs

Intersection of A002412 (hexagonal pyramidal) and A005408 (odd numbers).

Sequence in context: A367162 A360474 A327843 * A183521 A342109 A036337

Adjacent sequences: A015222 A015223 A015224 * A015226 A015227 A015228

Keyword

nonn,easy

Author

Mohammad K. Azarian

Extensions

More terms from Erich Friedman.

Status

approved