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A045891
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First differences of A045623.
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20
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1, 1, 3, 7, 16, 36, 80, 176, 384, 832, 1792, 3840, 8192, 17408, 36864, 77824, 163840, 344064, 720896, 1507328, 3145728, 6553600, 13631488, 28311552, 58720256, 121634816, 251658240, 520093696, 1073741824, 2214592512, 4563402752
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Let M_n be the n X n matrix m_(i,j)=3+abs(i-j) then det(M_n)=(-1)^(n+1)*a(n+1) - Benoit Cloitre (benoit7848c(AT)orange.fr), May 28 2002
If X_1,X_2,...,X_n are 2-blocks of a (2n+3)-set X then, for n>=1, a(n+2) is the number of (n+1)-subsets of X intersecting each X_i, (i=1,2,...,n). - Milan R. Janjic (agnus(AT)blic.net), Nov 18 2007
Equals row sums of triangle A152194 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 28 2008]
Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Aug 15 2010: (Start)
An elephant sequence, see A175655. For the central square 16 A[5] vectors, with decimal values between 19 and 400, lead to this sequence (without the first leading 1). For the corner squares these vectors lead to the companion sequence A045623.
(End)
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REFERENCES
| Paul Barry, A Catalan Transform and Related Transformations on Integer Sequences, Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.5.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Milan Janjic, Two Enumerative Functions
F. Ellermann, Illustration of binomial transforms
Index to sequences with linear recurrences with constant coefficients, signature (4,-4).
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FORMULA
| Sum_{ k = 0..n } (k+3)*binomial(n,k) gives the sequence with a different offset: 3, 7, 16, 36, 80, 176, 384, 832, 1792, 3840, 8192, ... - N. J. A. Sloane (njas(AT)research.att.com), Jan 30 2008
a(n) = (n+4)*2^(n-3), n >= 2; a(0)=1=a(1); G.f.: (1-x)^3/(1-2*x)^2.
Binomial transform of A027656.
Starting 1, 3, 7, 16.. this is ((n+5)2^n-0^n)/4, the binomial transform of (1, 2, 2, 3, 3, ...). - Paul Barry (pbarry(AT)wit.ie), May 20 2003
a(n)=(n+4)*2^(n-3)+3C(0, n)/4-C(1, n)/4; a(n)=sum{k=0..floor(n/2), C(n, 2k)(k+1)}. - Paul Barry (pbarry(AT)wit.ie), Nov 29 2004
a(n)=A045623(n-1)+2^n-2)=A034007(n+1)-2^(n-2) for n>=2 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Apr 20 2009]
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MATHEMATICA
| Join[{1, 1, a=3, b=7}, Table[c=4*b-4*a; a=b; b=c, {n, 100}]](*From Vladimir Joseph Stephan Orlovsky, Jan 15 2011*)
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PROG
| (PARI) v=[1, 1, 3, 7]; for(i=1, 99, v=concat(v, 4*(v[#v]-v[#v-1]))); v \\ Charles R Greathouse IV, Jun 01 2011
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CROSSREFS
| A152194 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 28 2008]
Sequence in context: A106463 A173514 * A081037 A019489 A077852 A020746
Adjacent sequences: A045888 A045889 A045890 * A045892 A045893 A045894
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KEYWORD
| easy,nonn,nice
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)
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