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Search: id:A005803
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| A005803 |
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Second-order Eulerian numbers: 2^n - 2n.
(Formerly M1838)
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+0
8
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| 1, 0, 0, 2, 8, 22, 52, 114, 240, 494, 1004, 2026, 4072, 8166, 16356, 32738, 65504, 131038, 262108, 524250, 1048536, 2097110, 4194260, 8388562, 16777168, 33554382, 67108812, 134217674, 268435400, 536870854, 1073741764, 2147483586
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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Also, number of 3 X n binary matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1), (01;0) and (01;1). An occurrence of a ranpp (xy;z) in a matrix A=(a(i,j)) is a triple (a(i1,j1), a(i1,j2), a(i2,j1)) where i1<i2, j1<j2, and these elements are in same relative order as those in the triple (x,y,z). - Sergey Kitaev (kitaev(AT)ms.uky.edu), Nov 11 2004
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REFERENCES
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I. Gessel and R. P. Stanley, Stirling polynomials, J. Combin. Theory, A 24 (1978), 24-33.
R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, Reading, MA, 1990, p. 256.
Klavzar, S.; Milutinovic, U.; and Petr, C., Hanoi graphs and some classical numbers, Expo. Math. 23 (2005), no. 4, 371-378.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..500
S. Kitaev, On multi-avoidance of right angled numbered polyomino patterns, Integers: Electronic Journal of Combinatorial Number Theory 4 (2004), A21, 20pp.
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures}, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Kitaev, On multi-avoidance of right angled numbered polyomino patterns, University of Kentucky Research Reports (2004).
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FORMULA
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G.f.: 1 + 2x^3/((1-x)^2(1-2x)). a(n)=A008517(n-1, 2). - Michael Somos, Oct 13, 2002
Equals binomial transform of [1, -1, 1, 1, 1,...]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 14 2008
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MAPLE
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a:=n->sum (2^j-2, j=2..n): seq(a(n), n=-1..30); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 27 2007
A005803:=-2*z/(2*z-1)/(z-1)**2; [Conjectured by S. Plouffe in his 1992 dissertation. Gives sequence except for three leading terms.]
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PROGRAM
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(PARI) a(n)=if(n<0, 0, 2^n-2*n)
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CROSSREFS
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a(n) = A070313 + 1 = A052515 + 2. Bisection of A077866.
Adjacent sequences: A005800 A005801 A005802 this_sequence A005804 A005805 A005806
Sequence in context: A006696 A094939 A006732 this_sequence A074352 A017928 A102880
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KEYWORD
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nonn,easy,nice
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AUTHOR
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njas, Simon Plouffe (plouffe(AT)math.uqam.ca)
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