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A218329 Even 9-gonal (nonagonal) pyramidal numbers. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A225276 A008527 A007584 * A009924 A297721 A019257

Adjacent sequences:  A218326 A218327 A218328 * A218330 A218331 A218332

KEYWORD

nonn

AUTHOR

Ant King, Oct 28 2012

STATUS

approved

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Last modified March 26 01:08 EDT 2019. Contains 321479 sequences. (Running on oeis4.)