A195309 - OEIS

%I #27 Jun 16 2017 02:55:39

%S 1,9,11,45,39,126,94,270,185,495,321,819,511,1260,764,1836,1089,2565,

%T 1495,3465,1991,4554,2586,5850,3289,7371,4109,9135,5055,11160,6136,

%U 13464,7361,16065,8739,18981,10279,22230,11990,25830,13881

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

%C The integers in same rows of the source triangle have a property related to Euler's Pentagonal Theorem.

%C Note that the column 1 of the mentioned triangle gives the positive terms of A001318 (see example).

%H G. C. Greubel, <a href="/A195309/b195309.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,4,0,-6,0,4,0,-1).

%F 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

%F 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

%e a(1) = 1

%e a(2) = 2+3+4 = 9

%e a(3) = 5+6 = 11

%e a(4) = 7+8+9+10+11 = 45

%e a(5) = 12+13+14 = 39

%e a(6) = 15+16+17+18+19+20+21 = 126

%e a(7) = 22+23+24+25 = 94

%e a(8) = 26+27+28+29+30+31+32+33+34 = 270

%e a(9) = 35+36+37+38+39 = 185

%p A195309 := proc(n)

%p         (n+1)*(9*n^2+18*n-1+(3*n^2+6*n+1)*(-1)^n)/32

%p end proc:

%p seq(A195309(n),n=1..60) ; # _R. J. Mathar_, Oct 08 2011

%t LinearRecurrence[{0,4,0,-6,0,4,0,-1},{1,9,11,45,39,126,94,270},80] (* _Harvey P. Dale_, Jun 22 2015 *)

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

%K nonn

%O 1,2

%A _Omar E. Pol_, Sep 21 2011