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Search: id:A096951
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| A096951 |
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Sum of odd powers of 2 and of 3 divided by 5. |
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+0
5
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| 1, 7, 55, 463, 4039, 35839, 320503, 2876335, 25854247, 232557151, 2092490071, 18830313487, 169464432775, 1525146340543, 13726182847159, 123535108753519, 1111813831298023, 10006315891747615, 90056808665990167
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OFFSET
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0,2
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COMMENT
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Sequence appears in A096952 (upper bounds for Lagrange remainder in Taylor expansion of ln((1+x)/(1-x)) for x=1/3, i.e. for ln(2).
Divisibility of 2^(2*n+1) + 3^(2*n+1) by 5 is proved by induction.
The sequence a(n+1), with g.f. (7-36x)/(1-13x+36x^2) and formula (27*9^n+8*4^n)/5, is the Hankel transform of C(n)+6*C(n+1), where C(n) is A000108(n). - Paul Barry (pbarry(AT)wit.ie), Dec 06 2006
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FORMULA
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a(n)=(2^(2*n+1) + 3^(2*k+1))/5.
G.f.: (1-6*x)/((1-4*x)*(1-9*x)).
a(n+1) = 4*a(n) + 3^(2*n+1), a(0) = 1. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 07 2008
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CROSSREFS
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Cf. A074614 for sum of even powers of 2 and of 3. A007689 for sum of powers of 2 and powers of 3.
a(n) = A138233(n)/5.
Adjacent sequences: A096948 A096949 A096950 this_sequence A096952 A096953 A096954
Sequence in context: A083068 A097189 A049028 this_sequence A113714 A078018 A108628
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Jul 16 2004
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