|
|
A115269
|
|
Row sums of correlation triangle for floor((n+4)/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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
Row sums of number triangle A115268.
|
|
LINKS
|
Index entries for linear recurrences with constant coefficients, signature (2,0,-2,3,-4,0,4,-3,2,0,-2,1).
|
|
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
|
|
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 *)
|
|
PROG
|
(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
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|