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Search: id:A015540
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| A015540 |
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Linear 2nd order recurrence. |
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+0
6
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| 0, 1, 5, 31, 185, 1111, 6665, 39991, 239945, 1439671, 8638025, 51828151, 310968905, 1865813431, 11194880585, 67169283511, 403015701065, 2418094206391, 14508565238345, 87051391430071, 522308348580425
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Number of walks of length n between any two distinct vertices of the complete graph K_7. Example: a(2)=5 because the walks of length 2 between the vertices A and B of the complete graph ABCDEFG are: ACB, ADB, AEB, AFB and AGB. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 01 2004
General form: k=6^n-k. Also: A001045, A078008, A097073, A115341, A015518, A054878, A015521, A109499, A015531, A109500 [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 11 2008]
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FORMULA
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a(n) = 5 a(n-1) + 6 a(n-2).
a(n)=6^n/7-(-1)^n/7. G.f.: x/((1-6x)(1+x)). E.g.f. (exp(6x)-exp(-x))/7. - Paul Barry (pbarry(AT)wit.ie), Apr 20 2003
a(n)=6^(n-1)-a(n-1). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 01 2004
a(n+1)=a(n)=sum{k=0..n, binomial(n-k, k)5^(n-2k)6^k} - Paul Barry (pbarry(AT)wit.ie), Jul 29 2004
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MATHEMATICA
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k=0; lst={k}; Do[k=6^n-k; AppendTo[lst, k], {n, 0, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 11 2008]
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PROGRAM
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(Other) sage: [lucas_number1(n, 5, -6) for n in xrange(0, 21)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 24 2009]
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CROSSREFS
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Partial sums are in A033116. Cf. A014987.
Cf. A001045, A078008, A097073, A115341, A015518, A054878, A015521, A109499, A015531, A109500 [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 11 2008]
Sequence in context: A078526 A137626 A057426 this_sequence A014987 A108079 A164038
Adjacent sequences: A015537 A015538 A015539 this_sequence A015541 A015542 A015543
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KEYWORD
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nonn,easy
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AUTHOR
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Olivier Gerard (olivier.gerard(AT)gmail.com)
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