|
| |
|
|
A317790
|
|
a(n) = 2*a(n-1) - a(n-2) + a(n-4) - 2*(n-5) + a(n-6) for n>5, a(0)=a(1)=1, a(2)=a(3)=7, a(4)=13, a(5)=19.
|
|
1
|
|
|
|
1, 1, 7, 7, 13, 19, 31, 37, 49, 61, 79, 91, 109, 127, 151, 169, 193, 217, 247, 271, 301, 331, 367, 397, 433, 469, 511, 547, 589, 631, 679, 721, 769, 817, 871, 919, 973, 1027, 1087, 1141, 1201, 1261, 1327, 1387, 1453, 1519, 1591, 1657, 1729, 1801, 1879, 1951
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,3
|
|
|
COMMENTS
|
a(n) is b(2*n) in A215175.
|
|
|
LINKS
|
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,-1,0,1,-2,1).
|
|
|
FORMULA
|
G.f.: (1 - x + 6*x^2 - 6*x^3 + 5*x^4 + x^5) / ((1 - x)^3*(1 + x)*(1 + x^2)). - Colin Barker, Aug 07 2018
a(n+1) = a(n) + 6*A059169(n+1).
a(2*k+1) = A003215(k).
From Bruno Berselli, Jul 08 2018: (Start)
a(2*k) = A016921(A000982(k)). More generally:
a(n) = (6*n^2 + 3*(3 - 2*(-1)^(n/2))*(1 + (-1)^n) + 2)/8. (End)
|
|
|
MATHEMATICA
|
CoefficientList[Series[(1 - x + 6 x^2 - 6 x^3 + 5 x^4 + x^5)/((1 - x)^3*(1 + x) (1 + x^2)), {x, 0, 51}], x] (* Michael De Vlieger, Aug 07 2018 *)
Table[(6 n^2 + 3 (3 - 2 (-1)^(n/2)) (1 + (-1)^n) + 2)/8, {n, 0, 60}] (* Bruno Berselli, Aug 08 2018 *)
|
|
|
PROG
|
(PARI) Vec((1 - x + 6*x^2 - 6*x^3 + 5*x^4 + x^5) / ((1 - x)^3*(1 + x)*(1 + x^2)) + O(x^60)) \\ Colin Barker, Aug 07 2018
|
|
|
CROSSREFS
|
Cf. A003215, A059169, A131729 (reverse order), A215175.
Cf. A000982, A016921.
Sequence in context: A072821 A038589 A332304 * A109539 A109541 A173314
Adjacent sequences: A317787 A317788 A317789 * A317791 A317792 A317793
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
Paul Curtz, Aug 07 2018
|
|
|
EXTENSIONS
|
Incorrect term 837 replaced with 817 by Colin Barker, Aug 07 2018
More terms from Colin Barker, Aug 07 2018
|
|
|
STATUS
|
approved
|
| |
|
|
