A218329 Even 9-gonal (nonagonal) pyramidal numbers.

10, 34, 80, 266, 420, 624, 1210, 1606, 2080, 3290, 4040, 4896, 6954, 8170, 9520, 12650, 14444, 16400, 20826, 23310, 25984, 31930, 35216, 38720, 46410, 50610, 55056, 64714, 69940, 75440, 87290, 93654, 100320, 114586, 122200, 130144, 147050, 156026, 165360

Offset

1,1

Links

Table of n, a(n) for n=1..39.

Index entries for linear recurrences with constant coefficients, signature (1, 0, 3, -3, 0, -3, 3, 0, 1, -1).

Formula

a(n) = a(n-1) + 3*a(n-3) - 3*a(n-4) - 3*a(n-6) + 3*a(n-7) + a(n-9) - a(n-10).

a(n) = 3*a(n-3) - 3*a(n-6) + a(n-9) + 448.

a(n) = phi(n)*(phi(n)+9)*(7*phi(n)-36)/4374, where phi(n) = 3 + 12*n - 3*cos(2*n*Pi/3) + sqrt(3)*sin(2*n*Pi/3).

G.f.: 2*x*(5+12*x+23*x^2+78*x^3+41*x^4+33*x^5+29*x^6+3*x^7)/((1-x)^4*(1+x+x^2)^3).

Example

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

Mathematica

LinearRecurrence[{1, 0, 3, -3, 0, -3, 3, 0, 1, -1}, {10, 34, 80, 266, 420, 624, 1210, 1606, 2080, 3290}, 39]

Crossrefs

Cf. A007584, A218328.

Sequence in context: A008527 A366415 A007584 * A009924 A297721 A019257

Adjacent sequences: A218326 A218327 A218328 * A218330 A218331 A218332

Keyword

nonn

Author

Ant King, Oct 28 2012

Status

approved