A195309 Row sums of an irregular triangle read by rows in which row n lists the next A026741(n+1) natural numbers A000027.

1, 9, 11, 45, 39, 126, 94, 270, 185, 495, 321, 819, 511, 1260, 764, 1836, 1089, 2565, 1495, 3465, 1991, 4554, 2586, 5850, 3289, 7371, 4109, 9135, 5055, 11160, 6136, 13464, 7361, 16065, 8739, 18981, 10279, 22230, 11990, 25830, 13881

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

Cf. A026741, A195310, A195311, A004188 (bisection).

Sequence in context: A345109 A143465 A201999 * A242507 A116152 A215831

Adjacent sequences: A195306 A195307 A195308 * A195310 A195311 A195312

Keyword

nonn

Author

Omar E. Pol, Sep 21 2011

Status

approved