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A033954
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n*(4*n+3). Also, second 10-gonal (or decagonal) numbers.
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25
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0, 7, 22, 45, 76, 115, 162, 217, 280, 351, 430, 517, 612, 715, 826, 945, 1072, 1207, 1350, 1501, 1660, 1827, 2002, 2185, 2376, 2575, 2782, 2997, 3220, 3451, 3690, 3937, 4192, 4455, 4726, 5005, 5292, 5587, 5890, 6201, 6520, 6847, 7182, 7525, 7876, 8235
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| S. M. Ellerstein, The square spiral, J. Recreational Mathematics 29 (#3, 1998) 188; 30 (#4, 1999-2000), 246-250.
R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, Reading, MA, 2nd ed., 1994, p. 99.
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LINKS
| Emilio Apricena, A version of the Ulam spiral
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FORMULA
| G.f.: x(7+x)/(1-x)^3. - Michael Somos, Mar 03 2003
a(n)=8*n+a(n-1)-1 with a(0)=0 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Jul 20 2010]
For n>0, a(n)^4+(a(n)+1)^4 +...+(a(n)+n)^4 +(4*A000217(n))^3 = (a(n)+n+1)^4+...+(a(n)+2n)^4; see also A045944 - Charlie Marion (charliemath(AT)optonline.net), Dec 8 2007
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EXAMPLE
| 16 17 18 19 ...
15 4 5 6 ...
14 3 0 7 ...
13 2 1 8 ...
For n=1, a(1)=8*1+0-1=7; n=2, a(2)=8*2+7-1=22; n=3, a(3)=8*3+22-1=45 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Jul 20 2010]
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MATHEMATICA
| s=0; lst={s}; Do[s+=n++ +7; AppendTo[lst, s], {n, 0, 7!, 8}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 16 2008]
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PROG
| (PARI) a(n)=4*n^2+3*n
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CROSSREFS
| Same as A033951 except start at 0. Cf. A002943.
a(n)=A001107(-n)=A074377(2n).
Sequences from spirals: A001107, A002939, A007742, A033951, A033952, A033953, A033954, A033989, A033990, A033991, A002943, A033996, A033988.
Cf. A002620.
Sequence in context: A031053 A063130 A171441 * A159227 A081274 A038764
Adjacent sequences: A033951 A033952 A033953 * A033955 A033956 A033957
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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