OFFSET
1,2
COMMENTS
The integers in same rows of the source triangle have a property related to Euler's Pentagonal Theorem.
Note that the column 1 of the mentioned triangle gives the positive terms of A001318 (see example).
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (0,4,0,-6,0,4,0,-1).
FORMULA
a(n) = (n+1)*(9*n^2+18*n-1+(3*n^2+6*n+1)*(-1)^n)/32 . - R. J. Mathar, Oct 08 2011
G.f. x*(1+9*x+7*x^2+9*x^3+x^4) / ( (x-1)^4*(1+x)^4 ). - R. J. Mathar, Oct 08 2011
EXAMPLE
a(1) = 1
a(2) = 2+3+4 = 9
a(3) = 5+6 = 11
a(4) = 7+8+9+10+11 = 45
a(5) = 12+13+14 = 39
a(6) = 15+16+17+18+19+20+21 = 126
a(7) = 22+23+24+25 = 94
a(8) = 26+27+28+29+30+31+32+33+34 = 270
a(9) = 35+36+37+38+39 = 185
MAPLE
A195309 := proc(n)
(n+1)*(9*n^2+18*n-1+(3*n^2+6*n+1)*(-1)^n)/32
end proc:
seq(A195309(n), n=1..60) ; # R. J. Mathar, Oct 08 2011
MATHEMATICA
LinearRecurrence[{0, 4, 0, -6, 0, 4, 0, -1}, {1, 9, 11, 45, 39, 126, 94, 270}, 80] (* Harvey P. Dale, Jun 22 2015 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Omar E. Pol, Sep 21 2011
STATUS
approved