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A027992
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a(n) = 1*T(n,0) + 2*T(n,1) + ... + (2n+1)*T(n,2n), T given by A027926.
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3
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1, 6, 22, 66, 178, 450, 1090, 2562, 5890, 13314, 29698, 65538, 143362, 311298, 671746, 1441794, 3080194, 6553602, 13893634, 29360130, 61865986, 130023426, 272629762, 570425346, 1191182338, 2483027970, 5167382530, 10737418242
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Also total sum of squares of parts in all compositions of n (offset 1). Total sum of cubes of parts in all compositions of n is (13*n-36)*2^(n-1)+6*n+18; total sum of fourth powers of parts in all compositions of n is (75*n-316)*2^(n-1)+12*n^2+72*n+158; total sum of fifth powers of parts in all compositions of n is (541*n-3060)*2^(n-1)+20*n^3+180*n^2+790*n+1530. - Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 18 2005
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REFERENCES
| Alejandro Erickson and Mark Schurch, Monomer-dimer tatami tilings of square regions, Arxiv preprint arXiv:1110.5103, 2011
Alejandro Erickson and Mark Schurch, Enumerating tatami mat arrangements of square grids, in 22nd International Workshop on Combinatorial Algorithms, University of Victoria, June 20-22, volume 7056 of Lecture Notes in Computer Science (LNCS), Springer Berlin / Heidelberg, 2011, pp. 223-235, DOI: 10.1007/978-3-642-25011-8_18
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FORMULA
| Conjectures: a(n) = 2^n*(3n-1)+2 = A048496(n+1)-1 = A053565(n+1)+2. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Jan 15 2004
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CROSSREFS
| Cf. A066183.
Sequence in context: A099855 A003469 A189418 * A171495 A178706 A159555
Adjacent sequences: A027989 A027990 A027991 * A027993 A027994 A027995
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KEYWORD
| nonn
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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