cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-10 of 12 results. Next

A155603 a(n) = 5^n+3^n-1.

Original entry on oeis.org

1, 7, 33, 151, 705, 3367, 16353, 80311, 397185, 1972807, 9824673, 49005271, 244672065, 1222297447, 6108298593, 30531927031, 152630937345, 763068593287, 3815084686113, 19074648589591, 95370918425025, 476847618556327
Offset: 0

Views

Author

Mohammad K. Azarian, Jan 25 2009

Keywords

Links

Crossrefs

Cf. A074501, A020515, A155588, A155590, A155592, A155593, A155594, A155596, A155597, A155598, A155599, A155600, A155601, A155602.

Programs

Formula

G.f.: 1/(1-5*x)+1/(1-3*x)-1/(1-x).
E.g.f.: e^(5*x)+e^(3*x)-e^x.
a(n) = 8*a(n-1)-15*a(n-2)-8 with a(0)=1, a(1)=7. - Vincenzo Librandi, Jul 21 2010
a(n) = A074606(n)-1. - R. J. Mathar, Mar 10 2022

A155607 9^n+3^n-1.

Original entry on oeis.org

1, 11, 89, 755, 6641, 59291, 532169, 4785155, 43053281, 387440171, 3486843449, 31381236755, 282430067921, 2541867422651, 22876797237929, 205891146443555, 1853020231898561, 16677181828806731, 150094635684419609
Offset: 0

Views

Author

Mohammad K. Azarian, Jan 25 2009

Keywords

Links

Crossrefs

Cf. A155596, A155597, A155598, A155599, A155600, A155601, A155602, A155603, A155604, A155605, A155606.

Programs

Formula

G.f.: 1/(1-9*x)+1/(1-3*x)-1/(1-x). E.g.f.: e^(9*x)+e^(3*x)-e^x.
a(n)=12*a(n-1)-27*a(n-2)-16 with a(0)=1, a(1)=11 - Vincenzo Librandi, Jul 21 2010

A155608 10^n + 3^n - 1.

Original entry on oeis.org

1, 12, 108, 1026, 10080, 100242, 1000728, 10002186, 100006560, 1000019682, 10000059048, 100000177146, 1000000531440, 10000001594322, 100000004782968, 1000000014348906, 10000000043046720, 100000000129140162
Offset: 0

Views

Author

Mohammad K. Azarian, Jan 25 2009

Keywords

Links

Crossrefs

Cf. A155596, A155597, A155598, A155599, A155600, A155601, A155602, A155603, A155604, A155605, A155606, A155607.

Programs

Formula

G.f.: 1/(1-10*x)+1/(1-3*x)-1/(1-x).
E.g.f.: e^(10*x)+e^(3*x)-e^x.
a(n) = 13*a(n-1)-30*a(n-2)-18 with a(0)=1, a(1)=12. - Vincenzo Librandi, Jul 21 2010

A155604 a(n) = 6^n + 3^n - 1.

Original entry on oeis.org

1, 8, 44, 242, 1376, 8018, 47384, 282122, 1686176, 10097378, 60525224, 362974202, 2177313776, 13062288338, 78368947064, 470199333482, 2821152954176, 16926788584898, 101560344088904, 609360902271962, 3656161926847376
Offset: 0

Views

Author

Mohammad K. Azarian, Jan 25 2009

Keywords

Links

Crossrefs

Cf. A074501, A020515, A155588, A155590, A155592, A155593, A155594, A155596, A155597, A155598, A155599, A155600, A155601, A155602, A155603.

Programs

Formula

G.f.: 1/(1-6*x)+1/(1-3*x)-1/(1-x).
E.g.f.: exp(6*x)+exp(3*x)-exp(x).
a(n) = 9*a(n-1)-18*a(n-2)-10 with a(0) = 1, a(1) = 8. - Vincenzo Librandi, Jul 21 2010

A155609 a(n) = 4^n - 3^n + 1.

Original entry on oeis.org

1, 2, 8, 38, 176, 782, 3368, 14198, 58976, 242462, 989528, 4017158, 16245776, 65514542, 263652488, 1059392918, 4251920576, 17050729022, 68332056248, 273715645478, 1096024843376, 4387586157902, 17560804984808, 70274600998838
Offset: 0

Views

Author

Mohammad K. Azarian, Jan 26 2009

Keywords

Comments

Let P(A) be the power set of an n-element set A and R be a relation on P(A) such that for all x, y of P(A), xRy if x and y are intersecting. Then a(n) = |R|. - Ross La Haye, Mar 19 2009

Links

Crossrefs

Cf. A155596, A155597, A155598, A155599, A155600, A155601, A155602, A155603, A155604, A155605, A155606, A155607, A155608.

Programs

Formula

G.f.: 1/(1-4*x) - 1/(1-3*x) + 1/(1-x).
E.g.f.: exp(4*x) - exp(3*x) + exp(x).
a(n) = 7*a(n-1)-12*a(n-2)+6 with a(0)=1, a(1)=2. - Vincenzo Librandi, Jul 21 2010

A155605 7^n+3^n-1.

Original entry on oeis.org

1, 9, 57, 369, 2481, 17049, 118377, 825729, 5771361, 40373289, 282534297, 1977503889, 13841818641, 96890604729, 678227855817, 4747575858849, 33232973616321, 232630643127369, 1628413985330937, 11398896347634609
Offset: 0

Views

Author

Mohammad K. Azarian, Jan 25 2009

Keywords

Links

Crossrefs

Cf. A155588, A155590, A155592, A155593, A155594, A155596, A155597, A155598, A155599, A155600, A155601, A155602, A155603, A155604.

Programs

Formula

G.f.: 1/(1-7*x)+1/(1-3*x)-1/(1-x). E.g.f.: e^(7*x)+e^(3*x)-e^x.
a(n)=10*a(n-1)-21*a(n-2)-12 with a(0)=1, a(1)=9 - Vincenzo Librandi, Jul 21 2010
a(0)=1, a(1)=9, a(2)=57, a(n)=11*a(n-1)-31*a(n-2)+21*a(n-3). - Harvey P. Dale, Nov 09 2012

A155610 5^n - 3^n + 1.

Original entry on oeis.org

1, 3, 17, 99, 545, 2883, 14897, 75939, 384065, 1933443, 9706577, 48650979, 243609185, 1219108803, 6098732657, 30503229219, 152544843905, 762810312963, 3814309845137, 19072324066659, 95363944856225, 476826697849923
Offset: 0

Views

Author

Mohammad K. Azarian, Jan 26 2009

Keywords

Links

Crossrefs

Cf. A155596, A155597, A155598, A155599, A155600, A155601, A155602, A155603, A155604, A155605, A155606, A155607, A155608, A155609.

Programs

Formula

G.f.: 1/(1-5*x)-1/(1-3*x)+1/(1-x).
E.g.f.: e^(5*x)-e^(3*x)+e^x.
a(n) = 8*a(n-1)-15*a(n-2)+8 with a(0)=1, a(1)=3. - Vincenzo Librandi, Jul 21 2010
a(0)=1, a(1)=3, a(2)=17, a(n)=9*a(n-1)-23*a(n-2)+15*a(n-3). - Harvey P. Dale, Jan 06 2012

A155606 a(n) = 8^n + 3^n - 1.

Original entry on oeis.org

1, 10, 72, 538, 4176, 33010, 262872, 2099338, 16783776, 134237410, 1073800872, 8590111738, 68720008176, 549757408210, 4398051294072, 35184386437738, 281475019757376, 2251799942825410, 18014398896902472, 144115189238117338
Offset: 0

Views

Author

Mohammad K. Azarian, Jan 25 2009

Keywords

Examples

			G.f. = 1 + 10*x + 72*x^2 + 538*x^3 + 4176*x^4 + 33010*x^5 + 262872*x^6 + ...

Links

Crossrefs

Cf. A155588, A155590, A155592, A155593, A155594, A155596, A155597, A155598, A155599, A155600, A155601, A155602, A155603, A155604, A155605.

Programs

Formula

G.f.: 1/(1-8*x) + 1/(1-3*x) - 1/(1-x).
E.g.f.: e^(8*x) + e^(3*x) - e^x.
a(n) = 11*a(n-1) - 24*a(n-2) - 14 with a(0)=1, a(1)=10. - Vincenzo Librandi, Jul 21 2010

A155612 7^n - 3^n + 1.

Original entry on oeis.org

1, 5, 41, 317, 2321, 16565, 116921, 821357, 5758241, 40333925, 282416201, 1977149597, 13840755761, 96887416085, 678218289881, 4747547161037, 33232887522881, 232630384847045, 1628413210489961, 11398894023111677
Offset: 0

Views

Author

Mohammad K. Azarian, Jan 26 2009

Keywords

Links

Crossrefs

Cf. A155596, A155597, A155598, A155599, A155600, A155601, A155602, A155603, A155604, A155605, A155606, A155607, A155608, A155609, A155610, A155611.

Programs

Formula

G.f.: 1/(1-7*x)-1/(1-3*x)+1/(1-x).
E.g.f.: e^(7*x)-e^(3*x)+e^x.
a(n) = 10*a(n-1)-21*a(n-2)+12 with a(0)=1, a(1)=5. - Vincenzo Librandi, Jul 21 2010

A155613 8^n - 3^n + 1.

Original entry on oeis.org

1, 6, 56, 486, 4016, 32526, 261416, 2094966, 16770656, 134198046, 1073682776, 8589757446, 68718945296, 549754219566, 4398041728136, 35184357739926, 281474933663936, 2251799684545086, 18014398122061496, 144115186913594406
Offset: 0

Views

Author

Mohammad K. Azarian, Jan 26 2009

Keywords

Links

Crossrefs

Cf. A155596, A155597, A155598, A155599, A155600, A155601, A155602, A155603, A155604, A155605, A155606, A155607, A155608, A155609, A155610, A155611, A155612.

Programs

Formula

G.f.: 1/(1-8*x)-1/(1-3*x)+1/(1-x).
E.g.f.: e^(8*x)-e^(3*x)+e^x.
a(n) = 11*a(n-1)-24*a(n-2)+14 with a(0)=1, a(1)=6. - Vincenzo Librandi, Jul 21 2010
Showing 1-10 of 12 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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