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A065874
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(7^(n+1) - (-6)^(n+1))/13.
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2
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1, 1, 43, 85, 1891, 5461, 84883, 314245, 3879331, 17077621, 180009523, 897269605, 8457669571, 46142992981, 401365114963, 2339370820165, 19196705648611, 117450280095541, 923711917337203, 5856623681349925, 44652524209512451
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| A second order recurrence of promic type (integer roots).
If the number j = A002378(m) is promic ( = i(i+1)), then a(n) = a(n-1)+j*a(n-2),a(0) = a(1) = 1 has a closed form solution involving only powers of integers. The binomial coefficient sum solves the recurrence regardless of promicity (cf. GKP reference)
Hankel transform is := 1,42,0,0,0,0,0,0,0,0,0,0,... [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 02 2008]
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REFERENCES
| R. L. Graham, D. E. Knuth, O. Patashnik, "Concrete Mathematics", Addison-Wesley, 1994, p. 204.
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LINKS
| Harry J. Smith, Table of n, a(n) for n = 0..150
Index to sequences with linear recurrences with constant coefficients, signature (1,42).
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FORMULA
| a(n)=a(n-1)+42a(n-2); a(0)=a(1)=1.
G.f.: -1/(6*x+1)/(7*x-1). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 16 2007
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MAPLE
| n->sum(binomial(n-k, k)*(42)^k, k=0..n)
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PROG
| (PARI) { for (n=0, 150, if (n>1, a=a1 + 42*a2; a2=a1; a1=a, a=a1=a2=1); write("b065874.txt", n, " ", a) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Nov 02 2009]
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CROSSREFS
| Cf. A001045 (j=2), A015441 (j=6), A053404 (j=12), A053428 (j=20), A053430 (j=30).
Sequence in context: A119487 A180549 A063351 * A062060 A037986 A198593
Adjacent sequences: A065871 A065872 A065873 * A065875 A065876 A065877
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KEYWORD
| nonn,easy
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AUTHOR
| Len Smiley (smiley(AT)math.uaa.alaska.edu), Dec 07 2001
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