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A248699 Expansion of (2 + x + 5*x^2 + 3*x^3 + 3*x^4 + x^5) / ((1 - x^3) * (1 - x^4)) in powers of x. 1
2, 1, 5, 5, 6, 7, 10, 9, 12, 12, 14, 15, 17, 16, 20, 20, 21, 22, 25, 24, 27, 27, 29, 30, 32, 31, 35, 35, 36, 37, 40, 39, 42, 42, 44, 45, 47, 46, 50, 50, 51, 52, 55, 54, 57, 57, 59, 60, 62, 61, 65, 65, 66, 67, 70, 69, 72, 72, 74, 75, 77, 76, 80, 80, 81, 82, 85 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..2500

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

FORMULA

G.f.: (2 + x + 5*x^2 + 3*x^3 + 3*x^4 + x^5) / ((1 - x^3) * (1 - x^4)).

a(n) = - A071047(-2-n) for all n in Z.

a(n+7) = a(n+4) + a(n+3) - a(n) for all n in Z.

a(n+3) = a(n) + [3, 5, 2, 5][mod(n, 4) + 1] for all n in Z.

a(n+4) = a(n) + [4, 6, 5][mod(n, 3) + 1] for all n in Z.

a(n+12) = a(n) + 15 for all n in Z.

a(n) = a(n-3) + a(n-4) - a(n-7). - Muniru A Asiru, Aug 01 2018

EXAMPLE

G.f. = 2 + x + 5*x^2 + 5*x^3 + 6*x^4 + 7*x^5 + 10*x^6 + 9*x^7 + 12*x^8 + ...

MAPLE

seq(coeff(series((2+x+5*x^2+3*x^3+3*x^4+x^5)/((1-x^3)*(1-x^4)), x, n+1), x, n), n=0..70); # Muniru A Asiru, Aug 01 2018

MATHEMATICA

a[ n_] := QUotient[ 5 n, 4] + { 0, 3, 2, 1, 1, 3, 1, 2, 1, 2, 2, 2}[[Mod[n, 12, 1]]];

CoefficientList[Series[(2 + x + 5*x^2 + 3*x^3 + 3*x^4 + x^5)/((1 - x^3)*(1 - x^4)), {x, 0, 50}], x]] (* G. C. Greubel, Aug 01 2018 *)

LinearRecurrence[{0, 0, 1, 1, 0, 0, -1}, {2, 1, 5, 5, 6, 7, 10}, 70] (* Robert G. Wilson v, Aug 01 2018 *)

PROG

(PARI) {a(n) = (5*n\4) + [ 2, 0, 3, 2, 1, 1, 3, 1, 2, 1, 2, 2][n%12 + 1]};

(PARI) {a(n) = polcoeff( if( n<0, n = -2-n; -(1 + 3*x + 3*x^2 + 5*x^3 + x^4 + 2*x^5), 2 + x + 5*x^2 + 3*x^3 + 3*x^4 + x^5) / ((1 - x^3) * (1 - x^4)) + x * O(x^n), n)};

(GAP) a:=[2, 1, 5, 5, 6, 7, 10];; for n in [8..70] do a[n]:=a[n-3]+a[n-4]-a[n-7]; od; a; # Muniru A Asiru, Aug 01 2018

CROSSREFS

Cf. A071047.

Sequence in context: A248797 A193536 A152290 * A032006 A167158 A074392

Adjacent sequences:  A248696 A248697 A248698 * A248700 A248701 A248702

KEYWORD

nonn,easy

AUTHOR

Michael Somos, Aug 01 2015

STATUS

approved

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Last modified April 12 21:13 EDT 2021. Contains 342932 sequences. (Running on oeis4.)