A144941 Numbers k such that 6*k-1 = A144796(k).

1, 36, 753, 41348, 868769, 47715364, 1002558481, 55063488516, 1156951618113, 63543218031908, 1335121164743729, 73328818545333124, 1540728667162644961, 84621393058096392996, 1777999546784527541073, 97653014260224692184068

Offset: 1

Author

Richard Choulet, Sep 26 2008

Keywords

• easy
• nonn

Comments

Also the index of a pentagonal number which is equal to the sum of two consecutive pentagonal numbers. - Colin Barker, Dec 22 2014

Examples

			a(1) = 1 because 6*1 - 1 = 5 = A144796(1).
		

Links

• Colin Barker, Table of n, a(n) for n = 1..653
• Index entries for linear recurrences with constant coefficients, signature (1,1154,-1154,-1,1).

Crossrefs

Cf. A133301, A144796, A144797.

Programs

GAP

a:=[1,36,753,41348,868769];; for n in [6..30] do a[n]:=a[n-1] +1154*a[n-2]-1154*a[n-3]-a[n-4]+a[n-5]; od; a; # G. C. Greubel, Mar 16 2019

Magma

R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( x*(1+ 35*x-437*x^2+205*x^3+4*x^4)/((1-x)*(1-34*x+x^2)*(1+34*x+x^2)) )); // G. C. Greubel, Mar 16 2019

Mathematica

LinearRecurrence[{1,1154,-1154,-1,1},{1,36,753,41348,868769},30] (* Harvey P. Dale, Dec 27 2018 *)

PARI

Vec(-x*(1+35*x-437*x^2+205*x^3+4*x^4) / ((x-1)*(x^2-34*x+1)*(x^2+34*x+1)) + O(x^30)) \\ Colin Barker, Dec 22 2014

Sage

a=(x*(1+ 35*x-437*x^2+205*x^3+4*x^4)/((1-x)*(1-34*x+x^2)*(1+34*x +x^2))).series(x, 30).coefficients(x, sparse=False); a[1:] # G. C. Greubel, Mar 16 2019

Formula

For the odd and even indices respectively the same recurrence is obtained: a(n+2) = 1154*a(n+1) - a(n) - 192.

We also have a(n+2) = 577*a(n+1) - 96 + 68*sqrt((72*a(n)^2-24*a(n)-32)).

G.f.: x*(1 + 35*x - 437*x^2 + 205*x^3 + 4*x^4) / ((1-x)*(1 - 34*x + x^2)*(1 + 34*x + x^2)). - R. J. Mathar, Nov 27 2011

Extensions

a(6) corrected and sequence extended by R. J. Mathar, Nov 27 2011