|
| |
|
|
A198392
|
|
a(n) = (6*n*(3*n+7)+(2*n+13)*(-1)^n+3)/16 + 1.
|
|
3
|
|
|
|
2, 4, 12, 18, 31, 41, 59, 73, 96, 114, 142, 164, 197, 223, 261, 291, 334, 368, 416, 454, 507, 549, 607, 653, 716, 766, 834, 888, 961, 1019, 1097, 1159, 1242, 1308, 1396, 1466, 1559, 1633, 1731, 1809, 1912, 1994, 2102, 2188, 2301, 2391, 2509, 2603, 2726, 2824, 2952
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,1
|
|
|
COMMENTS
|
For an origin of this sequence, see the triangular spiral illustrated in the Links section.
First bisection gives A117625 (without the initial term).
|
|
|
LINKS
|
Bruno Berselli, Table of n, a(n) for n = 0..1000
Bruno Berselli, Illustration of initial terms.
Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).
|
|
|
FORMULA
|
G.f.: (2+2*x+4*x^2+2*x^3-x^4)/((1+x)^2*(1-x)^3).
a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5).
a(n)-a(-n-1) = A168329(n+1).
a(n)+a(n-1) = A102214(n).
a(2n)-a(2n-1) = A016885(n).
a(2n+1)-a(2n) = A016825(n).
|
|
|
PROG
|
(PARI) for(n=0, 50, print1((6*n*(3*n+7)+(2*n+13)*(-1)^n+3)/16+1", "));
(MAGMA) [(6*n*(3*n+7)+(2*n+13)*(-1)^n+3)/16+1: n in [0..50]];
|
|
|
CROSSREFS
|
Cf. A152832 (by Superseeker).
Cf. sequences related to the triangular spiral: A022266, A022267, A027468, A038764, A045946, A051682, A062708, A062725, A062728, A062741, A064225, A064226, A081266-A081268, A081270-A081272, A081275 [incomplete list].
Sequence in context: A303403 A064407 A309519 * A052289 A309547 A309552
Adjacent sequences: A198389 A198390 A198391 * A198393 A198394 A198395
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
Bruno Berselli, Oct 25 2011
|
|
|
STATUS
|
approved
|
| |
|
|
