A060932
Fifth convolution of Lucas numbers A000032(n+1), n >= 0.
Original entry on oeis.org
1, 18, 159, 942, 4311, 16536, 55898, 171924, 491487, 1325546, 3409347, 8430246, 20164223, 46880424, 106350942, 236147828, 514553154, 1102562952, 2327442276, 4847463408, 9974081130, 20297335340
Offset: 0
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (6,-9,-10,30,6,-41,-6,30,10,-9,-6,-1).
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R:=PowerSeriesRing(Integers(), 40);
Coefficients(R!( ((1+2*x)/(1-x-x^2))^6 )); // G. C. Greubel, Apr 08 2021
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Table[((744+2990*n+2895*n^2+1925*n^3+825*n^4+125*n^5)*LucasL[n+2] +3*(256+390*n + 505*n^2+425*n^3+175*n^4+25*n^5)*LucasL[n+1])/(5^2*5!), {n,0,40}] (* G. C. Greubel, Apr 08 2021 *)
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def A060932_list(prec):
P. = PowerSeriesRing(ZZ, prec)
return P( ((1+2*x)/(1-x-x^2))^6 ).list()
A060932_list(40) # G. C. Greubel, Apr 08 2021
A060933
Sixth convolution of Lucas numbers A000032(n+1), n >= 0.
Original entry on oeis.org
1, 21, 217, 1498, 7910, 34566, 131446, 449732, 1416513, 4174765, 11651717, 31075422, 79751854, 198036146, 477899790, 1124785648, 2589534248, 5845989156, 12968091584, 28316428700, 60953528230, 129515454530, 271955244610, 564879359940, 1161646929275, 2366938010983, 4781794056543
Offset: 0
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (7,-14,-7,49,-14,-77,29,77,-14,-49,-7,14,7,1).
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R:=PowerSeriesRing(Integers(), 40);
Coefficients(R!( ((1+2*x)/(1-x-x^2))^7 )); // G. C. Greubel, Apr 08 2021
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m:= 40; S:= series( ((1+2*x)/(1-x-x^2))^7, x, m+1);
seq(coeff(S, x, j), j = 0..m); # G. C. Greubel, Apr 08 2021
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Table[(n+1)(2(100n^5+845n^4+2480n^3+4345n^2+5910n+2952)LucasL[n+2]+(125n^5+ 1030n^4+2995n^3+5930n^2+8280n+288)LucasL[n+1])/18000,{n,0,30}] (* Harvey P. Dale, Aug 13 2013 *)
CoefficientList[Series[((1+2x)/(1-x-x^2))^7, {x,0,30}], x] (* Vincenzo Librandi, Aug 13 2013 *)
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def A060930_list(prec):
P. = PowerSeriesRing(ZZ, prec)
return P( ((1+2*x)/(1-x-x^2))^7 ).list()
A060930_list(40) # G. C. Greubel, Apr 08 2021
Showing 1-2 of 2 results.