OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
a(n) = Sum_{i=0..n} (i + 1)*(3*i^2 + 3*i + 1).
a(n) = (3*n^4 + 6*n^3 + 3*n^2)/4 + 2*n^3 + 5*n^2 + 4*n + 1.
a(n) = (1/4)*(n + 1)^2*(n + 2)*(3*n + 2). - N-E. Fahssi, May 03 2008
G.f.: (1 + 10 x + 7 x^2)/(1 - x)^5. - N-E. Fahssi, May 03 2008
a(n) = Sum_{i=1..n} Sum_{j=1..n} Sum_{k=1..n} max(i,j,k). - Enrique Pérez Herrero, Feb 26 2013
E.g.f.: (3*x^4 + 32*x^3 + 86*x^2 + 56*x + 4)*exp(x)/4. - G. C. Greubel, Oct 23 2018
MAPLE
seq(coeff(series((1+10*x+7*x^2)/(1-x)^5, x, n+1), x, n), n = 0 .. 35); # Muniru A Asiru, Oct 24 2018
MATHEMATICA
Table[(3*n^4 + 14*n^3 + 23*n^2 + 16*n + 4)/4, {n, 0, 10}] (* G. C. Greubel, Oct 23 2018 *)
LinearRecurrence[{5, -10, 10, -5, 1}, {1, 15, 72, 220, 525}, 40] (* Harvey P. Dale, Mar 31 2022 *)
PROG
(Magma) [1/4*(n + 1)^2*(n + 2)*(3*n + 2): n in [0..30]]; // Vincenzo Librandi, May 16 2011
(PARI) vector(30, n, n--; (3*n^4+14*n^3+23*n^2+16*n+4)/4) \\ G. C. Greubel, Oct 23 2018
(GAP) List([0..35], n->(1/4)*(n+1)^2*(n+2)*(3*n+2)); # Muniru A Asiru, Oct 24 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Jonathan Vos Post, Mar 09 2007
EXTENSIONS
Corrected and extended by Vincenzo Librandi, May 16 2011
STATUS
approved