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A137215 a(n) = 3*(10^n) + (n*n+1)*((10^n)-1)/9. 0
3, 32, 355, 4110, 48887, 588886, 7111107, 85555550, 1022222215, 12111111102, 142222222211, 1655555555542, 19111111111095, 218888888888870, 2488888888888867, 28111111111111086, 315555555555555527, 3522222222222222190, 39111111111111111075, 432222222222222222182 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Sequence generalized: a(n) = a(0)*(B^n) + F(n)* ((B^n)-1)/(B-1); a(0), B integers, F(n) arithmetic function.

Examples:

a(0) = 1, B = 10, F(n) = 1 gives A002275, F(n) = 2 gives A090843, F(n) = 3 gives A097166, F(n) = 4 gives A099914, F(n) = 5 gives A099915.

a(0) = 1, B = 2, F(n) = 1 gives A000225, F(n) = 2 gives A033484, F(n) = 3 gives A036563, F(n) = 4 gives A048487, F(n) = 5 gives A048488, F(n) = 6 gives A048489.

a(0) = 1, B = 3, F(n) = 1 gives A003462, F(n) = 2 gives A048473, F(n) = 3 gives A134931, F(n) = 4 gives A058481, F(n) = 5 gives A116952.

a(0) = 1, B = 4, F(n) = 1 gives A002450, F(n) = 2 gives A020989, F(n) = 3 gives A083420, F(n) = 4 gives A083597, F(n) = 5 gives A083584.

a(0) = 1, B = 5, F(n) = 1 gives A003463, F(n) = 2 gives A057651, F(n) = 3 gives A117617, F(n) = 4 gives A081655.

a(0) = 2, B = 10, F(n) = 1 gives A037559, F(n) = 2 gives A002276.

LINKS

Table of n, a(n) for n=0..19.

Index entries for linear recurrences with constant coefficients, signature (33,-393,1991,-3930,3300,-1000).

FORMULA

a(n) = 3*(10^n) + (n*n+1)*((10^n)-1)/9.

O.g.f.: -(-3 + 67*x - 478*x^2 + 1002*x^3 - 850*x^4 + 100*x^5)/((-1+x)^3 * (-1+10*x)^3). - R. J. Mathar, Mar 16 2008

EXAMPLE

a(3) = 3*10^3 + (3*3 + 1)*(10^3 - 1)/9 = 4110.

PROG

(PARI) a(n) = 3*(10^n) + (n*n+1)*((10^n)-1)/9; \\ Jinyuan Wang, Feb 27 2020

CROSSREFS

Sequence in context: A037799 A091706 A091705 * A300366 A231591 A123336

Adjacent sequences:  A137212 A137213 A137214 * A137216 A137217 A137218

KEYWORD

nonn,easy

AUTHOR

Ctibor O. Zizka, Mar 06 2008

EXTENSIONS

More terms from R. J. Mathar, Mar 16 2008

More terms from Jinyuan Wang, Feb 27 2020

STATUS

approved

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Last modified April 10 02:39 EDT 2020. Contains 333392 sequences. (Running on oeis4.)