A323178 a(n) = 1 + 100*n^2 for n >= 0.

1, 101, 401, 901, 1601, 2501, 3601, 4901, 6401, 8101, 10001, 12101, 14401, 16901, 19601, 22501, 25601, 28901, 32401, 36101, 40001, 44101, 48401, 52901, 57601, 62501, 67601, 72901, 78401, 84101, 90001, 96101, 102401, 108901

Offset: 0

Author

Paul Curtz, Jan 06 2019

Keywords

• nonn

Comments

Terms of A261327 ending in 1 (01 for n > 0.)

a(n) mod 9 = period 9: repeat [1, 2, 5, 1, 8, 8, 1, 5, 2] = A275704(n+3).

(Analogous sequence: b(n) = 29 + 100*n*(n+1) = A261327(A017329) = 29, 229, 629, ... .)

Crossrefs

Cf. A000290, A008602 (20*n), A261327, A275704.

Subsequence of A017281.

Programs

Mathematica

a[n_] := 1 + 100*n^2 ; Array[a, 50, 0] (* or *)
CoefficientList[Series[(-1 - 98 x - 101 x^2)/(-1 + x)^3, {x, 0, 50}], x] (* or *)
CoefficientList[Series[E^x (1 + 100 x + 100 x^2), {x, 0, 50}], x]*Table[n!, {n, 0, 50}] (* Stefano Spezia, Jan 06 2019 *)

Formula

a(n) = A261327(A008602(n)).

Recurrence: a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2 with initial values a(0) = 1, a(1) = 101 and a(2) = 401.

From Stefano Spezia, Jan 06 2019: (Start)

O.g.f.: (-1 - 98*x - 101*x^2)/(-1 + x)^3.

E.g.f.: exp(x)*(1 + 100*x + 100*x^2).

(End)

Extensions

Corrected and extended (recurrence formula) by Werner Schulte, Feb 18 2019