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A063493 a(n) = (2*n-1)*(13*n^2-13*n+6)/6. 17
1, 16, 70, 189, 399, 726, 1196, 1835, 2669, 3724, 5026, 6601, 8475, 10674, 13224, 16151, 19481, 23240, 27454, 32149, 37351, 43086, 49380, 56259, 63749, 71876, 80666, 90145, 100339, 111274, 122976, 135471, 148785, 162944, 177974, 193901 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Harry J. Smith, Table of n, a(n) for n = 1..1000

T. P. Martin, Shells of atoms, Phys. Reports, 273 (1996), 199-241, eq. (10).

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

FORMULA

G.f.: x*(1+x)*(1+11*x+x^2)/(1-x)^4. - Colin Barker, Apr 20 2012

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>3. - Vincenzo Librandi, Dec 16 2015

E.g.f.: (-6 + 12*x + 39*x^2 + 26*x^3)*exp(x)/6 + 1. - G. C. Greubel, Dec 01 2017

MATHEMATICA

Table[(2 n - 1) (13 n^2 - 13 n + 6)/6, {n, 1, 40}] (* Bruno Berselli, Dec 16 2015 *)

LinearRecurrence[{4, -6, 4, -1}, {1, 16, 70, 189}, 30] (* G. C. Greubel, Dec 01 2017 *)

PROG

(PARI) { for (n=1, 1000, write("b063493.txt", n, " ", (2*n - 1)*(13*n^2 - 13*n + 6)/6) ) } \\ Harry J. Smith, Aug 23 2009

(PARI) x='x+O('x^30); Vec(serlaplace((-6+12*x+39*x^2+26*x^3)*exp(x)/6 + 1)) \\ G. C. Greubel, Dec 01 2017

(Python)

A063493_list, m = [], [26, -13, 2, 1]

for _ in range(10**2):

    A063493_list.append(m[-1])

    for i in range(3):

        m[i+1] += m[i] # Chai Wah Wu, Dec 15 2015

(MAGMA) [(2*n-1)*(13*n^2-13*n+6)/6: n in [1..40]]; // Vincenzo Librandi, Dec 16 2015

CROSSREFS

1/12*t*(2*n^3-3*n^2+n)+2*n-1 for t = 2, 4, 6, ... gives A049480, A005894, A063488, A001845, A063489, A005898, A063490, A057813, A063491, A005902, A063492, A005917, A063493, A063494, A063495, A063496.

Sequence in context: A211031 A200839 A036660 * A220212 A027997 A284844

Adjacent sequences:  A063490 A063491 A063492 * A063494 A063495 A063496

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Aug 01 2001

STATUS

approved

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Last modified January 20 10:23 EST 2018. Contains 297960 sequences.