A218328 Odd 9-gonal (nonagonal) pyramidal numbers.

1, 155, 885, 2639, 5865, 11011, 18525, 28855, 42449, 59755, 81221, 107295, 138425, 175059, 217645, 266631, 322465, 385595, 456469, 535535, 623241, 720035, 826365, 942679, 1069425, 1207051, 1356005, 1516735, 1689689, 1875315, 2074061, 2286375, 2512705

Offset

1,2

Links

Table of n, a(n) for n=1..33.

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

Formula

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

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + 448.

a(n) = (2*n-1)*(4*n-3)*(28*n-25)/3.

G.f.: x*(1+151*x+271*x^2+25*x^3)/(1-x)^4.

Example

The sequence of 9-gonal (nonagonal) pyramidal numbers A007584 begins 1, 10, 34, 80, 155, 266, 420, 624, 885, 1210, .... As the third odd term is 885, then a(3) = 885.

Mathematica

LinearRecurrence[{4, -6, 4, -1}, {1, 155, 885, 2639}, 33]

Prog

(PARI) a(n)=(2*n-1)*(4*n-3)*(28*n-25)/3 \\ Charles R Greathouse IV, Oct 18 2022

Crossrefs

Cf. A007584, A218329.

Sequence in context: A028382 A250936 A224336 * A101535 A010086 A110834

Adjacent sequences: A218325 A218326 A218327 * A218329 A218330 A218331

Keyword

nonn,easy

Author

Ant King, Oct 28 2012

Status

approved