A218327 Even octagonal pyramidal numbers (A002414).
30, 70, 364, 540, 1386, 1794, 3480, 4216, 7030, 8190, 12420, 14100, 20034, 22330, 30256, 33264, 43470, 47286, 60060, 64780, 80410, 86130, 104904, 111720, 133926, 141934, 167860, 177156, 207090, 217770, 252000, 264160, 302974, 316710, 360396, 375804, 424650
Offset: 1
Keywords
Examples
The sequence of octagonal pyramidal numbers A002414 begins 1, 9, 30, 70, 135, 231, 364, 540, 765, 1045, … As the third even term is 364, then a(3) = 364.
Links
- Index entries for linear recurrences with constant coefficients, signature (1, 3, -3, -3, 3, 1, -1).
Programs
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Mathematica
LinearRecurrence[{1,3,-3,-3,3,1,-1},{30,70,364,540,1386,1794,3480},37]
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)/8
G. f. 2*x(15+20*x+102*x^2+28*x^3+27*x^4)/((1-x)^4*(1+x)^3)