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A144941 Numbers k such that 6*k-1 = A144796(k). 1
1, 36, 753, 41348, 868769, 47715364, 1002558481, 55063488516, 1156951618113, 63543218031908, 1335121164743729, 73328818545333124, 1540728667162644961, 84621393058096392996, 1777999546784527541073, 97653014260224692184068 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

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).

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

EXAMPLE

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

MATHEMATICA

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

PROG

(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

(MAGMA) R<x>:=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

(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

(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

CROSSREFS

Cf. A133301, A144796, A144797.

Sequence in context: A327509 A215768 A320821 * A036084 A265194 A280123

Adjacent sequences:  A144938 A144939 A144940 * A144942 A144943 A144944

KEYWORD

easy,nonn

AUTHOR

Richard Choulet, Sep 26 2008

EXTENSIONS

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

STATUS

approved

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Last modified October 19 13:01 EDT 2019. Contains 328222 sequences. (Running on oeis4.)