A123177 -id:A123177 - cp's OEIS frontend

A123656 a(n) = 1 + n^4 + n^6.

3, 81, 811, 4353, 16251, 47953, 120051, 266241, 538003, 1010001, 1786203, 3006721, 4855371, 7567953, 11441251, 16842753, 24221091, 34117201, 47176203, 64160001, 85960603, 113614161, 148315731, 191434753, 244531251, 309372753, 387951931

Offset: 1

Jonathan Vos Post, Oct 04 2006

G. C. Greubel, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Cf. A001358, A002523, A091940, A123177, A123657-A123659.

[1 + n^4 + n^6: n in [1..25]]; // G. C. Greubel, Oct 17 2017

Table[1 + n^4 + n^6, {n, 1, 50}] (* G. C. Greubel, Oct 17 2017 *)
LinearRecurrence[{7,-21,35,-35,21,-7,1},{3,81,811,4353,16251,47953,120051},30] (* Harvey P. Dale, May 10 2020 *)

a(n)=1+n^4+n^6 \\ Charles R Greathouse IV, Oct 07 2015

a(n) = 1 + n^4 + n^6.

G.f.: x*(3 +60*x +307*x^2 +272*x^3 +81*x^4 -4*x^5 +x^6)/(1-x)^7. - Colin Barker, May 25 2012

A123659 a(n) = 1 + n^4 + n^6 + n^9 + n^10 + n^14.

Original entry on oeis.org

6, 18001, 4862512, 269750529, 6115250626, 78434755921, 678546021756, 4399254736897, 22880667197854, 100011001010001, 379778130741736, 1283985544700161, 3937524853545882, 11112316748827729, 29193541130581876

Offset: 1

Jonathan Vos Post, Oct 05 2006

G. C. Greubel, Table of n, a(n) for n = 1..1000

Cf. A001358, A002523, A091940, A123177, A123656-A123659.

[1 + n^4 + n^6 + n^9 + n^10 + n^14: n in [1..25]]; // G. C. Greubel, Oct 17 2017

Table[1 + n^4 + n^6 + n^9 + n^10 + n^14, {n, 1, 50}] (* G. C. Greubel, Oct 17 2017 *)

for(n=1,25, print1(1 + n^4 + n^6 + n^9 + n^10 + n^14, ", ")) \\ G. C. Greubel, Oct 17 2017

a(n) = 1 + n^4 + n^6 + n^9 + n^10 + n^14.

A123657 a(n) = 1 + n^4 + n^6 + n^9.

Original entry on oeis.org

4, 593, 20494, 266497, 1969376, 10125649, 40473658, 134483969, 387958492, 1001010001, 2359733894, 5162787073, 10609354744, 20668614737, 38454800626, 68736319489, 118612097588, 198393407569, 322734873982, 512064160001

Offset: 1

Jonathan Vos Post, Oct 04 2006

G. C. Greubel, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

Cf. A001358, A002523, A091940, A123177, A123656-A123659.

[1 + n^4 + n^6 + n^9: n in [1..25]]; // G. C. Greubel, Oct 17 2017

Table[1 + n^4 + n^6 + n^9, {n, 1, 50}] (* G. C. Greubel, Oct 17 2017 *)

a(n)=n^9+n^6+n^4+1 \\ Charles R Greathouse IV, Oct 16 2015

a(n) = 1 + n^4 + n^6 + n^9 = 1001010001 (base n).

G.f.: -x*(x^9 -8*x^8 -406*x^7 -14592*x^6 -88496*x^5 -156316*x^4 -87762*x^3 -14744*x^2 -553*x -4)/(x-1)^10. - Colin Barker, May 27 2012

A123665 a(n) = Sum_{k=1..21} n^A001358(k).

Original entry on oeis.org

22, 471260364628084305, 6457022669043550542502557676, 105149403852520725445003265581519105, 41911381174488637014293971538580334000626

Offset: 1

Jonathan Vos Post, Oct 04 2006

G. C. Greubel, Table of n, a(n) for n = 1..1000

Cf. A001358, A002523, A091940, A123177, A123656-A123665.

[1 + n^4 + n^6 + n^9 + n^10 + n^14 + n^15 + n^21 + n^22 + n^25 +
n^26 + n^33 + n^34 + n^35 + n^38 + n^39 + n^46 + n^49 + n^51 + n^55 + n^57 + n^58: n in [1..50]]; // G. C. Greubel, Oct 26 2017

Table[1 + n^4 + n^6 + n^9 + n^10 + n^14 + n^15 + n^21 + n^22 + n^25 +
  n^26 + n^33 + n^34 + n^35 + n^38 + n^39 + n^46 + n^49 + n^51 +
  n^55 + n^57 + n^58, {n, 1, 50}] (* G. C. Greubel, Oct 26 2017 *)

for(n=1,50, print1(1 + n^4 + n^6 + n^9 + n^10 + n^14 + n^15 + n^21 + n^22 + n^25 + n^26 + n^33 + n^34 + n^35 + n^38 + n^39 + n^46 + n^49 + n^51 + n^55 + n^57 + n^58, ", ")) \\ G. C. Greubel, Oct 26 2017

a(n) = 1 +n^4 +n^6 +n^9 +n^10 +n^14 +n^15 +n^21 +n^22 +n^25 +n^26 + n^33 +n^34 +n^35 +n^38 +n^39 +n^46 +n^49 +n^51 +n^55 +n^57 +n^58.

Better name from Joerg Arndt, May 23 2021

A123658 a(n) = 1 + n^4 + n^6 + n^9 + n^10.

Original entry on oeis.org

5, 1617, 79543, 1315073, 11735001, 70591825, 322948907, 1208225793, 3874742893, 11001010001, 28297158495, 67080151297, 148467846593, 309923269713, 615105191251, 1168247947265, 2134605998037, 3768860634193, 6453801131783, 10752064160001, 17474246985385

Offset: 1

Jonathan Vos Post, Oct 04 2006

			a(40) = 1+40^(A001358(1))+40^(A001358(2))+40^(A001358(3))+40^(A001358(4)) = 1+40^4+40^6+40^9+40^10 = 10747908098560001.

T. D. Noe, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

Cf. A001358, A002523, A091940, A123177, A123656-A123659.

[1+n^4+n^6+n^9+n^10: n in [0..50]]; // G. C. Greubel, Oct 17 2017

Table[1+n^4+n^6+n^9+n^10, {n,1,50}] (* G. C. Greubel, Oct 17 2017 *)
LinearRecurrence[{11,-55,165,-330,462,-462,330,-165,55,-11,1},{5,1617,79543,1315073,11735001,70591825,322948907,1208225793,3874742893,11001010001,28297158495},30] (* Harvey P. Dale, Jul 11 2025 *)

a(n)=1+n^4+n^6+n^9+n^10 \\ Charles R Greathouse IV, Oct 07 2015

a(n) = 1 + n^4 + n^6 + n^9 + n^10.

G.f.: x*(x^10 -8*x^9 +615*x^8 +33654*x^7 +381288*x^6 +1242534*x^5 +1378908*x^4 +528210*x^3 +62031*x^2 +1562*x +5)/(1-x)^11. - Colin Barker, May 27 2012

cp's OEIS Frontend

A123656 a(n) = 1 + n^4 + n^6.

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A123659 a(n) = 1 + n^4 + n^6 + n^9 + n^10 + n^14.

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A123657 a(n) = 1 + n^4 + n^6 + n^9.

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A123665 a(n) = Sum_{k=1..21} n^A001358(k).

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A123658 a(n) = 1 + n^4 + n^6 + n^9 + n^10.

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