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#11 by Alois P. Heinz at Fri Jan 09 20:59:24 EST 2015
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#10 by Jon E. Schoenfield at Fri Jan 09 20:57:08 EST 2015
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#9 by Jon E. Schoenfield at Fri Jan 09 20:57:06 EST 2015
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| NAME
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a(n) = 1+ + 2n+ + 3n^2+ + 4n^3.
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| FORMULA
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a(n) =() = (A053699(n+1)-) - A053699(n-1))/2- - 4n- - 1.
G.f.: (1+ + 6*x+ + 15*x^2+ + 2*x^3)/(1-x)^4. [. - _Colin Barker, _, Jan 10 2012]
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| EXAMPLE
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For n>4 this is 4321 translated from base n to base 10.
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| MATHEMATICA
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f[n_]:=1+2*n+3*n^2+4*n^3; lst={}; Do[AppendTo[lst, f[n]], {n, 0, 5!}]; lst [From _ (* _Vladimir Joseph Stephan Orlovsky_, Feb 12 2010] *)
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| CROSSREFS
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Note: 1+ + 2x+ + 3x^2+ + 4x^3 is the first derivative of 1+ + x+ + x^2+ + x^3+ + x^4, i.e. ., A053699. Cf. A000012, A005408, A056109, A056579.
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| STATUS
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approved
editing
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#8 by Russ Cox at Sat Mar 31 12:38:00 EDT 2012
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| MATHEMATICA
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f[n_]:=1+2*n+3*n^2+4*n^3; lst={}; Do[AppendTo[lst, f[n]], {n, 0, 5!}]; lst [From _Vladimir Joseph Stephan Orlovsky (4vladimir(AT)gmail.com), _, Feb 12 2010]
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Discussion
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| Sat Mar 31
| 12:38
| OEIS Server: https://oeis.org/edit/global/876
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#7 by Russ Cox at Fri Mar 30 18:51:27 EDT 2012
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| AUTHOR
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_Henry Bottomley (se16(AT)btinternet.com), _, Jun 29 2000
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Discussion
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| Fri Mar 30
| 18:51
| OEIS Server: https://oeis.org/edit/global/247
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#6 by Bruno Berselli at Tue Jan 10 11:48:31 EST 2012
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#5 by Colin Barker at Tue Jan 10 11:38:54 EST 2012
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#4 by Colin Barker at Tue Jan 10 11:38:49 EST 2012
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| FORMULA
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G.f.: (1+6*x+15*x^2+2*x^3)/(1-x)^4. [Colin Barker, Jan 10 2012]
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| STATUS
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approved
editing
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#3 by N. J. A. Sloane at Tue Jun 01 03:00:00 EDT 2010
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| MATHEMATICA
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f[n_]:=1+2*n+3*n^2+4*n^3; lst={}; Do[AppendTo[lst, f[n]], {n, 0, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Feb 12 2010]
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| KEYWORD
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easy,nonn,new
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#2 by N. J. A. Sloane at Fri May 16 03:00:00 EDT 2003
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| CROSSREFS
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Note: 1+2x+3x^2+4x^3 is derivative of 1+x+x^2+x^3+x^4 , , i.e. A053699. Cf. A000012, A005408, A056109, A056579.
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| KEYWORD
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easy,nonn,new
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| AUTHOR
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Henry Bottomley (se16@(AT)btinternet.com), Jun 29 2000
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