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A138190 Numerator of (n-1)*n*(n+1)/12. 4
0, 1, 2, 5, 10, 35, 28, 42, 60, 165, 110, 143, 182, 455, 280, 340, 408, 969, 570, 665, 770, 1771, 1012, 1150, 1300, 2925, 1638, 1827, 2030, 4495, 2480, 2728, 2992, 6545, 3570, 3885, 4218, 9139, 4940, 5330, 5740, 12341, 6622, 7095, 7590, 16215, 8648 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

a(n+2) is the numerator of A000295(n+2)/(3*int(t^n*(1-abs(1-t))^2,t=0..2)).

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, KirchhoffIndex

Index entries for linear recurrences with constant coefficients, signature (0,0,0,4,0,0,0,-6,0,0,0,4,0,0,0,-1).

FORMULA

a(n) = (n*(n-1)*(n+1)*(5+((-1)^n-(-1)^((2*n-1+(-1)^n)/4)-(-1)^((6*n-1+(-1)^n)/4))))/48. - Luce ETIENNE, Feb 17 2015

G.f.: x^2*(x^12 +2*x^11 +5*x^10 +10*x^9 +31*x^8 +20*x^7 +22*x^6 +20*x^5 +31*x^4 +10*x^3 +5*x^2 +2*x +1) / ((x -1)^4*(x +1)^4*(x^2 +1)^4). - Colin Barker, Feb 17 2015

EXAMPLE

0, 1/2, 2, 5, 10, 35/2, 28, 42, 60, 165/2, 110, 143, 182, ...

PROG

(PARI) a(n) = numerator((n-1)*n*(n+1)/12); \\ Michel Marcus, Feb 17 2015

(PARI) a(n)=binomial(n+1, 3)/if(n%4==2, 1, 2) \\ Charles R Greathouse IV, Feb 17 2015

CROSSREFS

Cf. A138191.

Sequence in context: A270521 A089073 A343167 * A056300 A326006 A144636

Adjacent sequences:  A138187 A138188 A138189 * A138191 A138192 A138193

KEYWORD

nonn,frac,easy

AUTHOR

Eric W. Weisstein, Mar 04 2008

STATUS

approved

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Last modified May 15 18:26 EDT 2021. Contains 343920 sequences. (Running on oeis4.)