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A146086 Number of n-digit numbers with each digit odd where the digits 1 and 3 occur an even number of times. 1
3, 11, 45, 197, 903, 4271, 20625, 100937, 498123, 2470931, 12295605, 61300877, 305972943, 1528270391, 7636568985, 38168496017, 190799433363, 953868026651, 4768952712765, 23843601302357, 119214519727383, 596062138283711, 2980279310358945, 14901302408615897 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..200

Index entries for linear recurrences with constant coefficients, signature (9,-23,15).

FORMULA

a(n) = (5^n+2*3^n+1)/4.

From Colin Barker, Dec 31 2013 (Start)

a(n) = 9*a(n-1)-23*a(n-2)+15*a(n-3).

G.f.: -x*(15*x^2-16*x+3) / ((x-1)*(3*x-1)*(5*x-1)). (End)

E.g.f.: exp(3*x)*(cosh(x))^2 - 1. - G. C. Greubel, Jan 31 2016

EXAMPLE

For n=2 the a(2)=11 numbers are 11, 33, 55, 57, 59, 75, 77, 79, 95, 97, 99.

MATHEMATICA

Table[(5^n + 2 3^n + 1)/4, {n, 1, 30}] (* Vincenzo Librandi, Dec 31 2013 *)

LinearRecurrence[{9, -23, 15}, {3, 11, 45}, 30] (* Harvey P. Dale, Dec 15 2014 *)

PROG

(PARI) a(n)=(5^n+2*3^n+1)/4; \\ Michel Marcus, Aug 22 2013

(MAGMA) [(5^n+2*3^n+1)/4: n in [1..30]]; // Vincenzo Librandi, Dec 31 2013

CROSSREFS

Sequence in context: A049160 A191243 A217888 * A049177 A217889 A217890

Adjacent sequences:  A146083 A146084 A146085 * A146087 A146088 A146089

KEYWORD

base,easy,nonn

AUTHOR

Jake Foster, Oct 27 2008

EXTENSIONS

More terms from Colin Barker, Dec 31 2013

STATUS

approved

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Last modified January 18 23:05 EST 2019. Contains 319282 sequences. (Running on oeis4.)