A198017 a(n) = n*(7*n + 11)/2 + 1.

1, 10, 26, 49, 79, 116, 160, 211, 269, 334, 406, 485, 571, 664, 764, 871, 985, 1106, 1234, 1369, 1511, 1660, 1816, 1979, 2149, 2326, 2510, 2701, 2899, 3104, 3316, 3535, 3761, 3994, 4234, 4481, 4735, 4996, 5264, 5539, 5821, 6110, 6406, 6709, 7019, 7336, 7660, 7991

Offset: 0

Author

Bruno Berselli, Oct 21 2011 - based on remarks and sequences by Omar E. Pol

Keywords

• nonn
• easy

Comments

First bisection of A193053 (see also the numerical spiral illustrated in the Links section).

The inverse binomial transform yields 1, 9, 7, 0, 0 (0 continued).

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 (3,-3,1).

Crossrefs

Cf. A195020 (vertices of the numerical spiral in link).

Cf. A017005 (first differences).

Cf. A069099, A001106.

Cf. A001106, A022264, A033572, A144555, A152760, A158482, A158485, A185019, A193053, A195021, A195023-A195030, A195320 [incomplete list].

Programs

Magma

[n*(7*n+11)/2+1: n in [0..47]];

Mathematica

Table[(n(7n+11))/2+1,{n,0,60}] (* or *) LinearRecurrence[{3,-3,1},{1,10,26},60] (* Harvey P. Dale, Mar 03 2013 *)

PARI

for(n=0, 47, print1(n*(7*n+11)/2+1", "));

Formula

G.f.: (1 + 7*x - x^2)/(1-x)^3.

a(n) = A195020(2*n) + 2*n + 1.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) = 2*a(n-1) - a(n-2) + 7.

From Elmo R. Oliveira, Dec 24 2024: (Start)

E.g.f.: exp(x)*(2 + 18*x + 7*x^2)/2.

a(n) = n + A001106(n+1). (End)