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A074605 3^n + 4^n. 5
2, 7, 25, 91, 337, 1267, 4825, 18571, 72097, 281827, 1107625, 4371451, 17308657, 68703187, 273218425, 1088090731, 4338014017, 17309009347, 69106897225, 276040168411, 1102998412177, 4408506864307, 17623567104025 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

a^n+b^n=(a+b)*a(n-1)-(a*b)*a(n-2) - Vincenzo Librandi, Jul 19 2010

REFERENCES

L. B. W. Jolley, "Summation of Series", Dover Publications, 1961, p. 14.

LINKS

B. Berselli, Table of n, a(n) for n = 0..1000. - Bruno Berselli, Jul 20 2010

Index entries for linear recurrences with constant coefficients, signature (7,-12).

FORMULA

2 + 7x + 25x^2 + 91x^3 +...n terms = (1 - 4^n*x^n)/(1 - 4x) + (1 - 3^n*x^n)/(1 - 3x). [Jolley] - Gary W. Adamson, Dec 20 2006

G.f.: 1/(1-3*x)+1/(1-4*x). E.g.f.: e^(3*x)+e^(4*x). - Mohammad K. Azarian, Jan 11 2009

a(n) = 3*a(n-1)+4^(n-1). - Bruno Berselli, Jul 20 2010

a(n)=7*a(n-1)-12*a(n-2) with a(0)=2, a(1)=7 - Vincenzo Librandi, Jul 19 2010

EXAMPLE

For n=2, a(2)=7*7-12*2=25: n=3, a(3)=7*25-12*7=91; n=4, a(4)=7*91-12*25=337.

MATHEMATICA

Table[3^n + 4^n, {n, 0, 25}]

PROG

(PARI) a(n)=3^n+4^n \\ Charles R Greathouse IV, Oct 07 2015

CROSSREFS

Cf. A000051, A034472, A052539, A034474, A062394, A034491, A062395, A062396, A007689, A063376, A063481, A074600-A074624.

Equals A074506(n) - 1.

Sequence in context: A108152 A024482 A097613 * A108081 A270785 A199247

Adjacent sequences:  A074602 A074603 A074604 * A074606 A074607 A074608

KEYWORD

easy,nonn

AUTHOR

Robert G. Wilson v, Aug 25 2002

STATUS

approved

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Last modified December 4 13:25 EST 2016. Contains 278750 sequences.