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A257601 a(n) = n^4/12+5*n^3/3+125*n^2/12+125*n/6+2. 1
2, 35, 100, 210, 380, 627, 970, 1430, 2030, 2795, 3752, 4930, 6360, 8075, 10110, 12502, 15290, 18515, 22220, 26450, 31252, 36675, 42770, 49590, 57190, 65627, 74960, 85250, 96560, 108955, 122502, 137270, 153330, 170755, 189620, 210002, 231980, 255635, 281050, 308310, 337502 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..40.

Yang-Hui He, John McKay, Sporadic and Exceptional, arXiv:1505.06742 [math.AG], 2015.

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

FORMULA

G.f.: (2+25*x-55*x^2+40*x^3-10*x^4)/(1-x)^5. - Vincenzo Librandi, Jun 08 2015

a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5). - Vincenzo Librandi, Jun 08 2015

MATHEMATICA

Table[n^4/12 + 5 n^3/3 + 125 n^2/12 + 125 n/6 + 2, {n, 0, 50] (* Bruno Berselli, Jun 08 2015 *)

LinearRecurrence[{5, -10, 10, -5, 1}, {2, 35, 100, 210, 380}, 50] (* Harvey P. Dale, Oct 21 2018 *)

PROG

(Sage) [n^4/12+5*n^3/3+125*n^2/12+125*n/6+2 for n in (0..50)] # Bruno Berselli, Jun 08 2015

(MAGMA) I:=[2, 35, 100, 210, 380]; [n le 5 select I[n] else 5*Self(n-1)-10*Self(n-2)+10*Self(n-3)-5*Self(n-4)+Self(n-5): n in [1..45]]; // Vincenzo Librandi, Jun 08 2015

CROSSREFS

Agrees with A257600 except for first term.

Sequence in context: A291162 A042459 A276713 * A282727 A042353 A193576

Adjacent sequences:  A257598 A257599 A257600 * A257602 A257603 A257604

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Jun 07 2015

STATUS

approved

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Last modified August 5 21:45 EDT 2021. Contains 346488 sequences. (Running on oeis4.)