A218326 Odd octagonal pyramidal numbers

1, 9, 135, 231, 765, 1045, 2275, 2835, 5049, 5985, 9471, 10879, 15925, 17901, 24795, 27435, 36465, 39865, 51319, 55575, 69741, 74949, 92115, 98371, 118825, 126225, 150255, 158895, 186789, 196765, 228811, 240219, 276705, 289641, 330855, 345415, 391645, 407925

Offset

1,2

Links

Table of n, a(n) for n=1..38.

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

Formula

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) + 384.

a(n) = (4*n-(-1)^n-1)*(4*n-(-1)^n-3)*(4*n-(-1)^n-4)/8.

G. f. x(1+8*x+123*x^2+72*x^3+159*x^4+16*x^5+5*x^6)/((1-x)^4*(1+x)^3).

Example

The sequence of octagonal pyramidal numbers A002414 begins 1, 9, 30, 70, 135, 231, 364, 540, 765, 1045, … As the third odd term is 135, then a(3) = 135.

Mathematica

LinearRecurrence[{1, 3, -3, -3, 3, 1, -1}, {1, 9, 135, 231, 765, 1045, 2275}, 38]

Crossrefs

Cf. A002414, A218327.

Sequence in context: A296171 A167893 A268062 * A272498 A254282 A235339

Adjacent sequences: A218323 A218324 A218325 * A218327 A218328 A218329

Keyword

nonn

Author

Ant King, Oct 27 2012

Status

approved