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A194455 a(n) = 2^n + 3n + 1. 5
2, 6, 11, 18, 29, 48, 83, 150, 281, 540, 1055, 2082, 4133, 8232, 16427, 32814, 65585, 131124, 262199, 524346, 1048637, 2097216, 4194371, 8388678, 16777289, 33554508, 67108943, 134217810, 268435541, 536871000, 1073741915, 2147483742 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Inverse binomial transform of this sequence: 2,4,1,1 (1 continued).

LINKS

Bruno Berselli, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,-5,2).

FORMULA

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

a(n) = A086653(n)-1  for n>0.

Sum(i=0..n, a(i)) = A115067(n+1)+2^(n+1).

a(n) = 3*a(n-1)-2*a(n-2)-3  for n>1.

a(n)^2 = 2^(n+1)*(a(n-1)+3)+(3*n+1)^2  for n>2.

MATHEMATICA

Table[2^n + 3 n + 1, {n, 0, 40}] (* Vincenzo Librandi, Mar 26 2013 *)

LinearRecurrence[{4, -5, 2}, {2, 6, 11}, 40] (* Harvey P. Dale, Oct 01 2014 *)

PROG

(MAGMA) [2^n+3*n+1: n in [0..31]];

(PARI) for(n=0, 31, print1(2^n+3*n+1", "));

CROSSREFS

Cf. A000051, A005126, A176691; A120845.

Cf. A062709 (first differences), A000079 (second and successive differences).

Cf. A146529 (differences between alternate terms, for n>2).

Sequence in context: A037258 A201993 A024521 * A163324 A048204 A259411

Adjacent sequences:  A194452 A194453 A194454 * A194456 A194457 A194458

KEYWORD

nonn,easy

AUTHOR

Bruno Berselli, Sep 01 2011

STATUS

approved

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Last modified June 23 21:29 EDT 2017. Contains 288675 sequences.