A115269 Row sums of correlation triangle for floor((n+4)/4).

1, 2, 4, 6, 11, 16, 24, 32, 46, 60, 80, 100, 130, 160, 200, 240, 295, 350, 420, 490, 581, 672, 784, 896, 1036, 1176, 1344, 1512, 1716, 1920, 2160, 2400, 2685, 2970, 3300, 3630, 4015, 4400, 4840, 5280, 5786, 6292, 6864, 7436, 8086, 8736, 9464, 10192, 11011, 11830

Offset: 0

Author

Paul Barry, Jan 18 2006

Keywords

• easy
• nonn

Comments

Row sums of number triangle A115268.

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Hamzeh Mujahed, Benedek Nagy, Hyper-Wiener Index on Rows of Unit Cells of the BCC Grid, Comptes rendus de l’Académie bulgare des Sciences, Tome 71, No 5, 2018, 675-684. See p. 8.
• Index entries for linear recurrences with constant coefficients, signature (2,0,-2,3,-4,0,4,-3,2,0,-2,1).

Programs

Mathematica

CoefficientList[Series[(1+x+x^2+x^3)^2/((1-x^4)^4(1-x^2)), {x,0,50}], x] (* Harvey P. Dale, Aug 20 2011 *)

PARI

a(n) = sum(k=0, n, sum(j=0, n, (j<=k)*((k-j+4)\4)*(j<=n-k)*((n-k-j+4)\4))); \\ Michel Marcus, Apr 09 2015

Formula

G.f.: (1+x+x^2+x^3)^2/((1-x^4)^4*(1-x^2));

a(n) = Sum_{k=0..n} Sum_{j=0..n} [j<=k]*floor((k-j+4)/4)*[j<=n-k]*floor((n-k-j+4)/4).

a(n) = 2*a(n-1) -2*a(n-3) +3*a(n-4) -4*a(n-5) +4*a(n-7) -3*a(n-8) +2*a(n-9) -2*a(n-11) +a(n-12).

G.f.: -1 / ( (x^2+1)^2*(1+x)^3*(x-1)^5 ). - R. J. Mathar, Nov 28 2014

a(n) = (2*(n^4+24*n^3+197*n^2+636*n)+3*(431+(2*n^2+24*n+65)*(-1)^n)+24*((n+7)*(-1)^((2*n-1+(-1)^n)/4)-(n+5)*(-1)^((6*n-1+(-1)^n)/4)))/1536. - Luce ETIENNE, Mar 03 2015

Extensions

More terms from Michel Marcus, Apr 09 2015