A032795 Positive numbers k such that (k+1)*(k+2)*(k+3)*(k+4)/(k+(k+1)+(k+2)+(k+3)+(k+4)) is an integer.

8, 18, 56, 126, 176, 312, 504, 624, 918, 1292, 1512, 2024, 2640, 2990, 3780, 4698, 5208, 6336, 7616, 8316, 9842, 11544, 12464, 14448, 16632, 17802, 20304, 23030, 24480, 27560, 30888, 32648, 36366, 40356, 42456, 46872, 51584, 54054, 59228

Offset: 1

Author

Patrick De Geest, May 15 1998

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (1,0,3,-3,0,-3,3,0,1,-1).

Crossrefs

Cf. A032793, A032794.

Programs

Magma

R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( 2*x*(4+ 5*x +19*x^2+23*x^3+10*x^4+11*x^5+3*x^6)/((1-x)*(1-x^3)^3) )); // G. C. Greubel, May 29 2019

Mathematica

CoefficientList[Series[2*x*(4+5x+19x^2+23x^3+10x^4+11x^5+3x^6)/((1-x)^4*(1+x+x^2)^3), {x, 0, 39}], x] (* Georg Fischer, May 27 2019 *)

PARI

Vec(2*x*(4+5*x+19*x^2+23*x^3+10*x^4+11*x^5+3*x^6)/((1-x)^4*(1+x+x^2)^3) + O(x^20)) \\ Felix Fröhlich, May 27 2019

Sage

a=(2*x*(4+ 5*x +19*x^2+23*x^3+10*x^4+11*x^5+3*x^6)/((1-x)*(1-x^3)^3) ).series(x, 30).coefficients(x, sparse=False); a[1:] # G. C. Greubel, May 29 2019

Formula

a(n) = A032794(n)/A032793(n).

O.g.f.: 2*x*(4+5*x+19*x^2+23*x^3+10*x^4+11*x^5+3*x^6)/((1-x)^4* (1+x+x^2)^3). [Corrected by Georg Fischer, May 27 2019]

Extensions

Definition amended and offset changed by Georg Fischer, May 27 2019