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, 2753499
Offset: 1
Examples
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.
Links
- Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
Programs
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Mathematica
LinearRecurrence[{4,-6,4,-1},{1,155,885,2639},33] -
PARI
a(n)=(2*n-1)*(4*n-3)*(28*n-25)/3 \\ Charles R Greathouse IV, Oct 18 2022
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.
E.g.f.: 25 + exp(x)*(224*x^3 + 192*x^2 + 78*x - 75)/3. - Elmo R. Oliveira, Aug 24 2025